The present invention relates to the field of simulation of networked processes, and more particularly, to the simulation of a continuous fluid model having a discrete time evolution.
The ability to meet supply commitments is becoming more and more the important differentiating factor of suppliers besides product quality and price. Meeting supply commitments is essential for suppliers especially in a fast paced business with short product life cycles and high volatile demands.
Semiconductor manufacturing as a supplier of camcorder, computer or Gameboy assembly lines is a typical examples of such a chain link in the supply chain of the fast paced consumer electronic industry. Therefore, production management and control in this area must be provided with a planning methodology and tools that allow predicting the movement of work in process and the manufacturing output for a certain period of time in the future.
A planning tool must react instantly and efficiently to variations and changes of a production process, such as machine outages, general machine problems, increased rework rates, varying customer orders, and the like. Specially, in a semiconductor production line such a planning task is challenging. On the one hand, the production process itself is complex and typically features hundreds or even thousands of process steps that need to be performed in a highly interactive manner. On the other hand, typically, a large variety of products with different process flows are processed in parallel. Moreover, such a planning tool can be applied universally to a variety of networked processes that are executed by a plurality of stations, each of which dedicated to execute a specific task. In this way, the planning tool allows planning and simulating a variety of networked processes, such as production processes in manufacturing lines or networked tasks performed, e.g., by various computer systems.
By making use of discrete event simulation tools, the movement of work in process and manufacturing outputs of a production line can, in principle, be forecasted. However, discrete event simulation is time consuming and requires large computing resources. For instance, for a discrete event simulation, it may take several hours to run the simulation of a large manufacturing line, even when using state of the art computing resources. This is due to the empirical nature of the discrete event simulation, i.e., the intermediate products in the production process are treated as discrete entities on a continuous timeframe. By way of example, when a supply chain equally splits into two different production stations, at least two discrete supply events must be simulated in order to account for the equal splitting.
Another approach for simulating production processes is based on a continuous fluid model that is discrete in time. Here, the discrete nature of a manufacturing line is disregarded and the complexity of the simulation model is effectively reduced to an analytical model. As an advantage, this analytical model can be evaluated within a short period of time. Even though the continuous approach is not intuitive, in a build-to-plan production environment, a work piece, such as a wafer, needs not be treated individually. Alternatively, work pieces of the same order and the same product can be combined into volumes and do not need to be considered as individuals either. Hence, they do not differ from a manufacturing point of view. Typically, they follow the same process flow and they can be handled by the same machines with the same process times and featuring the same rework probability.
Therefore, from a scheduling perspective, it is not necessary to determine a certain sequence of individuals, but rather calculate the average amount of work pieces that have to be processed at a certain work station within a certain period of time. This can be achieved by assigning a certain amount of machine capacity to work pieces of a certain product within a certain period of time, which finally yielded to the idea of fluid models.
The publication “Dynamic scheduling of a multi class fluid network” by H. Chen and D. D. Yao, Operations Research, 41:1104-1115, 1993 describes a multi-class fluid network consisting of a plurality of stations, among which several classes of fluids are circulated and processed. At each station, the input flow comes from both external sources as well as internal transitions (including feedbacks), and the output flow goes to other stations or leaves the network following a flow-transfer matrix. Here, the scheduling control of fluid networks can be solved systematically through a sequence of linear programming problems. The control problem is formulated to minimize a linear inventory cost over the entire spectrum, referred to global optimum. Aiming for such a global optimum provides a vehicle to solve the problem: it naturally suggests a systematic solution via a sequence of linear programs, referred to ‘myopic procedure’, which generates a piece-wise optimum solution. That is, the solution spanning over the entire spectrum is obtained by pasting a finite plurality of pieces; each local optimum being only optimum with respect to its initial state. Further, it is shown that if a global optimum solution exists, it is guaranteed to be generated by the myopic procedure.
Hence, the scheduling of control of fluid networks makes particular use of linear programming and optimization approaches. On the one hand, such an optimization approach requires appreciable computing resources and computing time. On the other, these optimization approaches have basically objective functions with coefficients reflecting the inventory costs associated with a work piece. In particular, in large manufacturing lines a large amount of those cost coefficients need to be defined, which in turn requires manual gathering and continuous maintenance of the cost coefficients.
The present invention therefore aims at providing a simulation of a production process on the basis of a continuous fluid model featuring a shorter simulation time and requiring less computing resources. Moreover, the invention aims to provide autonomous acquisition of input data for the fluid model.